As far as anyone knows, RSA is just as secure if everyone uses the same encryption exponent e (which is part of the public key). Common values of e are 3 and 65537.

The choice of e = 3 is the smallest value of e that can work [2 is not relatively prime to (p-1)(q-1)] and public key operations only require two multiplications.

There are some potential problems with e = 3. First, suppose the message M is smaller than N^1/3, where N is the modulus. Then the encrypted M is just M³, and a cube root attack will break the message.

Second, suppose the same message M is encrypted for three different users. Then an attacker sees

     M³ mod N₁
     M³ mod N₂
     M³ mod N₃

and he can use the Chinese Remainder Theorem to find

     M³ mod (N₁⋅N₂⋅N₃)

and the cube root attack will recover M.

In practice, these are not serious problems, since we can simply pad a message (which is usually a short secret key) with random bits.

Also, for e = 3 to work, 3 must be relatively prime to φ(N) for each modulus N.

Another popular value is e = 65537 = 2¹⁶+1, which requires only 17 multiplications for public key operations. This value has somewhat similar, though less severe, "issues" as e = 3. For example, the same message must be sent to 65537 users before the "Chinese remainder" attack discussed above can work.